Question

In Argand diagram all the complex numbers z satisfying $|z-4i|+|z+4i|=10$ lie on a :

• A. Straight line
• B. Circle
• C. Ellipse
• D. Parabola

Answer 1

Answer: (C)

Ellipse

$|z-4i|$ distance of 'z' from '4i'
$|z+4i|$ distance of 'z' from '-4i'
$\therefore |z-4i|+|z+4i|=10$ represents all those 'z' whose sum of distances from two fixed points is constant i.e. 10 This the precisely the definition of an ellipse.
$\to$ The two fixed points are the two focis of the ellipse
$\to$ The constant sum ($=10$) is the length of the major axis